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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 11, Issue 2

Issues

Substituting compact disks in stable planes

Rainer Löwen
  • Institut für Analysis und Algebra, Technische Universität Braunschweig, Pockelsstraße 14, 38106 Braunschweig, Germany
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Published Online: 2011-04-08 | DOI: https://doi.org/10.1515/advgeom.2010.047

Abstract

Given two stable planes of dimension 2l containing compact topological 2l-disks whose boundaries are isomorphic unitals, we show that it is possible to substitute one of these disks with the other, thus changing the line system in one of the planes, and that this produces another stable plane. The proof uses intersection theory in singular homology in order to show that existence of interior intersection points of two secants can be detected by looking at their traces in the unital. We conclude with a class of concrete examples based on P. Sperner's 4-dimensional affine planes with group .

About the article

Received: 2010-09-08

Published Online: 2011-04-08

Published in Print: 2011-04-01


Citation Information: Advances in Geometry, Volume 11, Issue 2, Pages 337–346, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.047.

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[1]
Markus Stroppel
Journal of Geometry, 2011, Volume 102, Number 1-2, Page 179
[2]
Steffen Poppitz and Markus Stroppel
Advances in Geometry, 2011, Volume 11, Number 2

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